System and method for determining a representation of an acoustic field

ABSTRACT

This system for determining a representation of an acoustic field (P) includes: 
         acoustic wave acquisition elements ( 1 ) including a plurality of elemental sensors ( 2   1  to  2   Q ) which are distributed in space and which each deliver a measurement signal (c 1  to c Q ); and    elements ( 8 ) for processing by the application, to the measurement signals (c 1  to c Q ), of filtering combinations representative of structural characteristics of the acquisition elements ( 1 ) in order to deliver a plurality of acoustic signals (sc 1  to sc N ) which are each associated with a predetermined general reproduction direction defined relative to a given point in space ( 14 ), the set of acoustic signals (sc 1  to sc N ) forming a representation of the acoustic field (P). The system is characterized in that the elemental sensors ( 2   1  to  2   Q ) are distributed in space in a substantially non-regular manner and in that the filtering combinations are representative of that distribution.

The present invention relates to a method, a device and a system fordetermining a representation of an acoustic field in the form of aplurality of acoustic or audiophonic signals which are each associatedwith a predetermined general reproduction direction defined relative toa given point in space.

The determination of such a representation is based on the use ofacoustic wave acquisition means comprising a plurality of elementalsensors which are arranged in space and which each deliver a measurementsignal.

Those measurement signals are processed by applying filteringcombinations, which are representative, in particular, of structuralcharacteristics of the acquisition means and of the predeterminedgeneral reproduction directions, in order to obtain the plurality ofacoustic signals.

Such a plurality of signals is commonly referred to by the expression“multichannel signal” and corresponds to a plurality of signals, called“channels”, which are transmitted in parallel or multiplexed with eachother. Each of the signals is intended for a reproduction element or agroup of reproduction elements forming an ideal source arranged in ageneral direction predefined relative to a given point in space.

For example, a conventional multichannel standard known by the name “5.1ITU-R BF 775-1” comprises five channels intended for reproductionelements placed in five predetermined general directions defined by theangles 0°, +30°, −30°, +110° and −110° relative to the listening centre.

Such an arrangement therefore corresponds to the arrangement of aloudspeaker or a group of loudspeakers at the front in the centre, oneon each side at the front on the left and the right and one on each sideat the rear on the left and the right.

The application of the acoustic signals to reproduction elementsarranged in appropriate predetermined general directions theoreticallypermits the reproduction of an acoustic field.

Acquisition and processing constitute key elements in the quality ofthis reproduction.

Some existing acquisition means are formed by a set of directionalelemental sensors where each sensor delivers directly a channelcorresponding to one of the predetermined general reproductiondirections. In that case, each sensor is substantially oriented in thedirection corresponding to its associated channel.

The quality of the representation obtained with such acquisition meansis limited by the intrinsic directivity of the sensors, because noprocessing is carried out, so that the representation is not arepresentation of high quality.

Other techniques, such as the techniques grouped under the term“ambisonic”, are based on a modeling of the acquisition means in theform of a punctiform set of elemental and directional sensors so as toconsider only the directions of origin of the sounds relative to thecentre of the acquisition means.

However, the impossibility of positioning the set of elemental sensorsat the same point, the absence of elemental sensors having enhanceddirectivity characteristics and also the simplicity of the processingcarried out, such as gain matrices, restrict these technologies to arepresentation whose quality is limited to the level of precisioncommonly referred to as “order 1” on the basis of the sphericalharmonics.

Finally, the system described in the article entitled “Circularmicrophone array for discrete multichannel audio recording”, presentedon 22 Mar. 2003 at the 114^(th) convention of the AES, uses a circularregular network of 288 cardioid microphones. Complex processing inseveral steps of all of the signals delivered by this network of sensorsenables a high-quality representation of the acoustic field to beobtained.

It therefore appears that the existing acquisition and processing meansrequire a large amount of regularly distributed elemental sensors andalso complex processing in order to arrive at a high-qualityrepresentation of the acoustic field in a multichannel format.

This substantially reduces the portability of these systems andincreases the cost of implementation and the calculation times.

The object of the invention is to solve those problems by providing amethod, a device and a system for determining a high-qualityrepresentation of an acoustic field in a multichannel format, which areof enhanced portability and rapidity and which are inexpensive.

To that end, the invention relates to a system for determining arepresentation of an acoustic field of the type comprising:

acoustic wave acquisition means comprising a plurality of elementalsensors which are distributed in space and which each deliver ameasurement signal; and

means for processing by the application, to the measurement signals, offiltering combinations representative of structural characteristics ofthe acquisition means in order to deliver a plurality of acousticsignals which are each associated with a predetermined generalreproduction direction defined relative to a given point in space, theset of acoustic signals forming a representation of the acoustic field,

characterized in that the elemental sensors are distributed in space ina substantially non-regular manner and in that the filteringcombinations are representative of that distribution.

According to other features:

the acquisition means are such that, for all of the usual coordinatesystems, for at least one of the coordinates of the coordinate system,the values of the coordinates of the positions of all of the elementalsensors are distributed on distinct values and at a non-constant pitch;

the acquisition means comprise at least one omnidirectional elementalsensor;

the acquisition means comprise at least one elemental sensor whosedirectivity is a combination of omnidirectional and bidirectionalpatterns;

the acquisition means comprise a number of elemental sensors of one tofive times the number of predetermined general reproduction directions;

the processing means comprise a single matrix filtering stage receivingas an input the measurement signals and delivering as an output theplurality of acoustic signals;

the processing means form weighted linear combinations of themeasurement signals in order to form the acoustic output signals;

the processing means permit the application of filtering combinationswhich vary with the frequency of the measurement signals processed.

The invention relates also to a device for determining a representationof an acoustic field, which device comprises means for processing thesignals delivered by acoustic wave acquisition means comprising aplurality of elemental sensors distributed in space, by applyingfiltering combinations representative of structural characteristics ofthe acquisition means in order to deliver a plurality of acousticsignals which are each associated with a predetermined generalreproduction direction defined relative to a given point in space, theacoustic signals forming a representation of the acoustic field,characterized in that the processing means are suitable for processingsignals delivered by acquisition means formed by sensors distributed inspace in a substantially non-regular manner.

The invention relates also to a method for determining a representationof an acoustic field, characterized in that it comprises:

a step of acquiring, at a plurality of points distributed in space in asubstantially non-regular manner, the acoustic field by acoustic waveacquisition means in order to deliver a plurality of measurement signalswhich are representative at each point, in amplitude and in phase, ofthe acoustic field;

a step of processing by applying, to the measurement signals, filteringcombinations representative of structural characteristics of theacquisition means in order to deliver a plurality of acoustic signalswhich are each associated with a predetermined general reproductiondirection defined relative to a given point in space, the set ofacoustic signals forming a representation of the acoustic field.

According to other features of the method of the invention,

the processing step corresponds to:

-   -   the application to the measurement signals of filtering        combinations in order to generate a plurality of processed        signals constituting a representation of the acoustic field        which is substantially independent of the structural        characteristics of the acquisition means, in the form of a        finite number of Fourier-Bessel coefficients; and    -   the application to the processed signals of specific linear        combinations in order to generate the corresponding plurality of        acoustic signals;

the processing step corresponds to the application of filteringcombinations in accordance with a technique selected from the groupformed:

-   -   by filtering techniques in the frequency domain;    -   by filtering techniques in the temporal domain by impulse        response; and    -   by filtering techniques in the temporal domain by means of        infinite impulse response recursive filters.

The invention relates also to a method for checking the non-regularcharacter of a network of elemental sensors, characterized in that itconsists:

in considering the network in a first usual coordinate system;

in checking the values of the positions of all of the sensors inaccordance with a first coordinate of the coordinate system;

if the values of the first coordinates are neither constant nordistributed at regular intervals, the network is called non-regular inthe current coordinate system and the method is repeated in anothercoordinate system;

if the values of the first coordinates are either constant ordistributed at regular intervals, the values of the positions of thesensors are checked in accordance with a second coordinate of thecoordinate system;

if the values of the second coordinates are neither constant nordistributed at regular intervals, the network is non-regular in thecurrent coordinate system and the method is repeated with anothercoordinate system;

if the values of the second coordinates are either constant ordistributed at regular intervals, the values of the positions of thesensors are checked in accordance with a third coordinate of thecoordinate system;

if the values of the third coordinates are neither constant nordistributed at regular intervals, the network is non-regular in thecurrent coordinate system and the method is repeated in anothercoordinate system;

if, for the first, second and third coordinates, the values of thecoordinates of the positions of all of the sensors are either constantor distributed at regular intervals, the network is regular in thecurrent coordinate system;

if, in any one of the usual coordinate systems, the network is regular,it is called regular; and

if the network is non-regular in each of the usual coordinate systems,it is called non-regular.

The invention will be better understood on reading the followingdescription which is given purely by way of example and with referenceto the appended drawings in which:

FIG. 1 is a representation of a spherical coordinate system;

FIG. 2 is a block diagram of a reproduction system according to theinvention;

FIG. 3 is a flow chart of the method of the invention; and

FIG. 4 is a detailed representation of the processing performed by theinvention.

FIG. 1 shows a conventional spherical coordinate system in order toclarify the coordinate system to which reference is made in the text.

This coordinate system is an orthonormal coordinate system having anorigin O and comprising three axes (OX), (OY) and (OZ). In thiscoordinate system, a position indicated {right arrow over (x)} isdescribed by means of it spherical coordinates (r,θ,φ), where r denotesthe distance relative to the origin O, θ the orientation in the verticalplane and φ the orientation in the horizontal plane.

In such a coordinate system, an acoustic field is known if the acousticpressure indicated p(r,θ,φ,t), whose Fourier transform is indicatedP(r,θ,φ,ƒ) where ƒ denotes the frequency, is defined at all points ateach instant t.

The method of the invention is based on the use of spatio-temporalfunctions enabling any-acoustic field to be described in time and in thethree spatial dimensions.

In the embodiments described, these functions are what are known asspherical Fourier-Bessel functions of the first kind which will bereferred to hereinafter as Fourier-Bessel functions.

In a region empty of sources and empty of obstacles, the Fourier-Besselfunctions correspond to the solutions of the wave equation andconstitute a basis which generates all of the acoustic fields producedby sources located outside this region.

Any three-dimensional acoustic field can therefore be expressed by alinear combination of the Fourier-Bessel functions in accordance withthe expression of the inverse Fourier-Bessel transform which isexpressed:${P\left( {r,\theta,\phi,f} \right)} = {4\pi{\sum\limits_{l = 0}^{\infty}{\sum\limits_{m = {- 1}}^{l}{{P_{l,m}(f)}j^{l}{j_{l}({kr})}{y_{l}^{m}\left( {\theta,\phi} \right)}}}}}$

In that equation, the terms P_(l,m)(ƒ) are defined as the Fourier-Besselcoefficients of the field p(r,θ,φ,t), ${k = \frac{2\pi\quad f}{c}},$c is the speed of sound in air (340 ms⁻¹), j_(l)(kr) is the sphericalBessel function of the first kind and of order l defined by${j_{l}(x)} = {\sqrt{\frac{\pi}{2x}}{J_{l + {1/2}}(x)}}$where J_(ν)(x) is the Bessel function of the first kind and of order ν,and γ_(l) ^(m)(θ,φ) is the real spherical harmonic of order l and ofterm m, with m ranging from −l to l, defined by:y_(l)^(m)(θ, ϕ) = P_(l)^(m)(cos   θ)trg_(m)(ϕ)${{with}:{{trg}_{m}(\phi)}} = \left\{ \begin{matrix}{\frac{1}{\sqrt{\pi}}{\cos\left( {m\quad\phi} \right)}} & {{{pour}\quad m} > 0} \\\frac{1}{\sqrt{2\pi}} & {{{pour}\quad m} = 0} \\{\frac{1}{\sqrt{\pi}}{\sin\left( {m\quad\phi} \right)}} & {{{pour}\quad m} < 0}\end{matrix} \right.$

In this equation, the P_(m)(x) are the associated Legendre functionsdefined by:${P_{l}^{m}(x)} = {\sqrt{\frac{{2l} + 1}{2}}\sqrt{\frac{\left( {l - m} \right)!}{\left( {l + m} \right)!}}\left( {1 - x^{2}} \right)^{m/2}\frac{\mathbb{d}^{m}}{\mathbb{d}x^{m}}{P_{l}(x)}}$

with P_(l)(x) denoting the Legendre polynomials, defined by:${P_{l}(x)} = {\frac{1}{2^{l} \cdot {l!}}\frac{\mathbb{d}^{l}}{\mathbb{d}x^{l}}\left( {x^{2} - 1} \right)^{l}}$

The Fourier-Bessel coefficients are also expressed in the temporaldomain by the coefficients p_(l,m)(t) corresponding to the inversetemporal Fourier transform of the coefficients P_(l,m)(ƒ).

In other embodiments, the acoustic field is broken down on the basis offunctions, where each of the functions is expressed by an optionallyinfinite linear combination of Fourier-Bessel functions.

FIG. 2 shows schematically a system according to the invention.

This system comprises acquisition means 1 formed by Q elemental sensors2 ₁ to 2 _(Q) delivering measurement signals c₁(t) to c_(Q)(t), alsoindicated c₁ to c_(Q), which are introduced into a device 6 fordetermining a representation of an acoustic field.

The device 6 comprises processing means 8 suitable for applying to themeasurement signals c₁ to c_(Q) filtering combinations representative ofstructural characteristics of the acquisition means 1, in order todeliver as an output a plurality of acoustic signals which are eachassociated with a predetermined general reproduction direction definedrelative to a given point in space.

The acoustic signals sc₁(t) to sc_(N)(t), also indicated sc₁ to sc_(N),delivered by the device 6, are then transmitted to reproduction means 10comprising N reproduction elements 12 ₁ to 12 _(N) arranged inpredetermined directions relative to a given point 14 in space,corresponding to the centre of the reproduction means 10.

The control of these reproduction elements 12 ₁ to 12 _(N) by theacoustic signals sc₁ to sc_(N), enables the acoustic field picked up bythe acquisition means 1 to be reproduced.

Preferably, the processing means 8 of the device 6 are configuredbeforehand and are associated specifically with a set of elementalsensors 2 ₁ to 2 _(Q) forming the acquisition means 1 and with a set ofreproduction elements forming the reproduction means 10.

Advantageously, however, the processing means 8 comprise a plurality offiltering combinations which correspond to different acquisition meansand/or to different output formats and which can be selected by a user,for example directly by means of a switch or through a controlinterface.

The device 6 may be in the form of electronic equipment dedicated to theimplementation of the invention or in the form of software comprisingprogram code instructions which are to be executed by equipmentcomprising a processor and means for interfacing with acquisition meansand reproduction means.

For example, the device 6 is formed by a computer associated withsuitable interface cards.

The elemental sensors 2 ₁ to 2 _(Q) are located at known points in spacearound a predetermined point 4 designated as the centre of theacquisition means 1.

Thus, the position (r_(q),θ_(q),φ_(q)) of each elemental sensor 2 _(q)is expressed in space in a spherical coordinate system, such as thatdescribed with reference to FIG. 1, centred on the centre 4 of theacquisition means 1.

According to the invention, the elemental sensors 2 ₁ to 2 _(Q) aredistributed in space in a substantially non-regular manner.

For a given configuration, or a network, to be regarded as non-regularin space, it is necessary, for all of the usual three-dimensionalcoordinate systems, whether they be Cartesian, cylindrical or spherical,for at least one of the coordinates of the coordinate system, that thevalues of the coordinates of the positions of all of the elementalsensors should be neither constant nor distributed at a constant pitch,that is to say, distributed on distinct values and at a non-constantpitch.

Or, a configuration is non-regular if, for all of the usual coordinatesystems, for at least one of the three coordinates of the coordinatesystem, the values of the coordinates of the positions of all of thesensors are distributed in a non-zero spatial domain or interval andwith a variable deviation of the coordinates taken in succession.

Thus, configurations in which the sensors are arranged at regularintervals along a line or circle, at the intersections of an imaginaryflat grid or at the intersections of an imaginary cubic mesh, areregular configurations.

It will be appreciated that the evaluation of such a non-regulardistribution must take into account a tolerance resulting from theconstraints of physical production and the constraints associated withthe dimensioning of the elemental sensors used.

Therefore, the coordinates of the sensors must be distributed in aninterval greater than a tolerance interval and must have deviationsbeyond that tolerance interval.

In general, the position of a sensor corresponds to the position of thecentre of its sensitive portion and a tolerance interval in each spatialdirection is defined around that position.

Advantageously, the tolerance interval for a set of elemental sensorsforming the acquisition means corresponds to a distance equivalent toone quarter of the distance between the two elemental sensors that areclosest together. For example, such a distance is of the order of 2 cm,so that the tolerance interval corresponds approximately to 0.5 cm.

Conversely, a configuration is considered to be regular if, in one ofthe usual coordinate systems, for the three coordinates of that system,the values of coordinates of the positions of all of the sensors areconstant or distributed at a constant pitch.

Or, a configuration is regular if, in one of the usual coordinatesystems, for all of the coordinates of that system, the values ofcoordinates of the positions of all of the sensors are distributed in asubstantially zero interval or with a substantially constant successivedeviation.

In addition, sensors that have a substantially non-zero physical spacerequirement and that are placed next to one another form a punctiform oralmost punctiform distribution which is regarded as a regularconfiguration.

The following method makes it possible to determine whether a givenconfiguration of elemental sensors is regular or non-regular.

The above-mentioned configuration is considered with reference to afirst of the three usual coordinate systems, such as thethree-dimensional Cartesian coordinate system.

The values of the positions of all of the sensors are then checked inaccordance with a first coordinate of the coordinate system, such as theabscissa. If those values are neither constant nor distributed atregular intervals, taking into account a tolerance interval, then theconfiguration is non-regular in this coordinate system and the procedureis started again with another coordinate system.

If the values of these first coordinates are either constant ordistributed at regular intervals, the values of the positions of thesensors are checked in accordance with a second coordinate of thecoordinate system, such as the ordinate.

If the values of these second coordinates are neither constant nordistributed at regular intervals, the configuration is non-regular inthis coordinate system and the procedure is started again with anothercoordinate system.

Conversely, if the values of these coordinates are either constant ordistributed at regular intervals, the values of the positions of thesensors are checked in accordance with the third and last coordinate ofthe coordinate system, such as that according to a vertical axis calledthe zenith coordinate.

If the values of these third coordinates are neither constant nordistributed at regular intervals, the configuration is non-regular inthis coordinate system and the procedure is started again with anothercoordinate system.

In the opposite case, in this coordinate system, for all of thecoordinates, the values of the coordinates of the positions of all ofthe sensors are either constant or distributed at regular intervals.Therefore, the configuration is regular in this coordinate system.

At the end of the tests in the three usual coordinate systems, if theconfiguration is regular in one of the three coordinate systems, it iscalled regular. Conversely, if the configuration is non-regular in thethree coordinate systems, it is called non-regular.

Such a substantially non-regular distribution avoids the redundancy ofthe data sampled by the elemental sensors in the acoustic field, withthe result that a reduced number of sensors is necessary.

Advantageously, the maximum number Q of elemental sensors is less thanor equal to five times the number of acoustic signals forming therepresentation of the acoustic field at the end of the processingoperation.

Furthermore, the distribution of the elemental sensors 2 _(q) in spacemay comply with specific rules while at the same time complying with thecriteria of non-regularity such as defined above.

Advantageously, the acquisition means 1 reproduce the generalgeometrical characteristics of the reproduction means 10, such as aplanar arrangement and a given symmetry, while respecting the criteriaof non-regularity.

With reference to FIGS. 3 and 4, a description will now be given of theoperation of the system of the invention.

Before implementing the invention, the acquisition means 1 are arrangedin space in a substantially non-regular manner.

During a first step 20 of acquisition, the system of the invention isexposed to an acoustic field P and each sensor 2 _(q) of the acquisitionmeans 1 delivers a measurement signal c_(q)(t) which corresponds to themeasurement made by that sensor in the acoustic field P.

The acquisition means 1 therefore deliver a plurality of measurementsignals of the acoustic field c₁(t) to c_(Q)(t), which are associateddirectly with the acquisition capacities of the elemental sensors 2 ₁ to2 _(Q).

The method then includes a step 30 of processing by the application offiltering combinations to the measurement signals c₁ to c_(Q) deliveredby the acquisition means 1.

As indicated above, these filtering combinations are representative ofthe structural characteristics of the acquisition means 1 and aresuitable for delivering a plurality of acoustic signals sc₁ to sc_(N)which are each associated with a predetermined general reproductiondirection defined relative to a given point in space.

More especially, the N channels sc₁(t) to sc_(N)(t) are obtained fromthe Q measurement signals c₁(t) to c_(Q)(t) by means of a single matrixfiltering involving N×Q filters varying as a function of the frequency,and indicated T_(n,q)(ƒ). Each output channel sc₁(t) is obtained byfiltering each of the measurement signals c₁(t) to c_(Q)(t) and byapplying a linear combination to the signals thus filtered.

Each filter T_(n,q)(ƒ) is therefore representative of the contributionof the measurement signal c_(q)(t) in the constitution of the channelsc_(n)(t). The channels are obtained in accordance with therelationship:${{SC}_{n}(f)} = {\sum\limits_{q = 1}^{Q}{{T_{n,q}(f)}{C_{q}(f)}}}$

In that relationship, SC_(n)(ƒ) is the Fourier transform of sc_(n)(t)and C_(q)(ƒ) is the Fourier transform of c_(q)(t).

The filters T_(n,q)(ƒ) may be organized in a matrix T of size N×Q in thefollowing manner: $T = \begin{bmatrix}{T_{1,1}(f)} & {T_{1,2}(f)} & \cdots & {T_{1,Q}(f)} \\{T_{2,1}(f)} & {T_{2,2}(f)} & \cdots & {T_{2,Q}(f)} \\\vdots & \vdots & \quad & \vdots \\{T_{N,1}(f)} & {T_{N,2}(f)} & \cdots & {T_{N,Q}(f)}\end{bmatrix}$

In the embodiment described, the matrix T is obtained by means of thefollowing matrix relationship:T=DE

In that equation, E is an encoding matrix representative of thecharacteristics of the acquisition means 1 and in particular of theirspatial configuration. The matrix E makes it possible to obtain arepresentation, in Fourier Bessel coefficients, of an acoustic field{tilde over (P)} corresponding to an estimate of the acoustic field P inwhich the elemental sensors 2 ₁ to 2 _(Q), are immersed, on the basis ofthe measurement signals c₁(t) to c_(Q)(t). The matrix E has the size(L+1)²×Q, the coefficient L corresponding to the order at which theencoding is carried out and to the maximum resolution that the encodingenables to be achieved. The matrix E is obtained by means of therelationship:E=μB ^(T)(μBB ^(T)+(1−μ)I _(N))⁻¹In that equation, the coefficient μ specifies a compromise between thefidelity of representation of the acoustic field {tilde over (P)} andthe minimization of the background noise introduced by the elementalsensors 2 ₁ to 2 _(Q) and may assume any of the values between 0 and 1.Thus, if μ=0, the background noise is minimal and if μ=1, the spatialquality is maximum.

Advantageously, the parameters L and μ can vary with the frequency.

In that relationship, B is a spatial sampling matrix of size Q×(L+1)²whose elements B_(q,l,m)(ƒ) are organized in the following manner:$\begin{bmatrix}{B_{1,0,0}(f)} & {B_{1,1,{- 1}}(f)} & {B_{1,1,0}(f)} & {B_{1,1,1}(f)} & \cdots & {B_{1,L,{- L}}(f)} & \cdots & {B_{1,L,0}(f)} & \cdots & {B_{1,L,L}(f)} \\{B_{2,0,0}(f)} & {B_{2,1,{- 1}}(f)} & {B_{2,1,0}(f)} & {B_{2,1,1}(f)} & \cdots & {B_{2,L,{- L}}(f)} & \cdots & {B_{2,L,0}(f)} & \cdots & {B_{2,L,L}(f)} \\\vdots & \vdots & \vdots & \vdots & \quad & \vdots & \quad & \vdots & \quad & \vdots \\{B_{Q,0,0}(f)} & {B_{Q,1,{- 1}}(f)} & {B_{Q,1,0}(f)} & {B_{Q,1,1}(f)} & \cdots & {B_{Q,L,{- L}}(f)} & \cdots & {B_{Q,L,0}(f)} & \cdots & {B_{Q,L,L}(f)}\end{bmatrix}\quad$

If all of the elemental sensors 2 ₁ to 2_(Q) are sensors of theomnidirectional type, the term B is expressed in the following manner:B _(q,l,m)(ƒ)=4πj ^(l) j _(l)(kr _(q))γ_(l) ^(m)(θ_(q),φ_(q))

In that relationship, (r_(q),θ_(q),φ_(q)) is the position of the sensor2 _(q) in the spherical coordinate system described with reference toFIG. 1.

In other embodiments, each sensor 2 _(q) is placed at the position(r_(q),θ_(q),φ_(q)), has a directivity composed of a combination ofomnidirectional and bidirectional patterns of proportion d_(q) and isoriented in the direction (θ_(q) ^(α),φ_(q) ^(α)), so that the sensor 2_(q) has a maximum sensitivity in the direction (θ_(q) ^(α),φ_(q) ^(α)).In that case, the elements B_(q,l,m)(ƒ) are obtained in the followingmanner: $\begin{matrix}{{B_{n,l,m}(f)} = {4\pi\quad j^{l} \times \left\{ {{\left( {1 - d_{q}} \right){j_{l}\left( {kr}_{q} \right)}{y_{l}^{m}\left( {\theta_{q},\phi_{q}} \right)}} - {{jd}_{q} \times}} \right.}} \\{\left( {{{j_{l}^{*}\left( {kr}_{q} \right)}{y_{l}^{m}\left( {\theta_{q},\phi_{q}} \right)}u_{r}} - {\frac{j_{l}\left( {kr}_{q} \right)}{{kr}_{q}}{R_{l}^{m}\left( {\cos\quad\theta_{q}} \right)}{{trg}_{m}\left( \phi_{q} \right)}u_{\theta}} +} \right.} \\\left. \left. {\frac{{mj}_{l}\left( {kr}_{q} \right)}{{kr}_{q}\sin\quad\theta_{q}}{y_{l}^{- m}\left( {\theta_{q},\phi_{q}} \right)}u_{\phi}} \right) \right\}\end{matrix}$${{where}:\text{}{j_{l}^{*}\left( {kr}_{q} \right)}} = \frac{{{lj}_{l - 1}\left( {kr}_{q} \right)} - {\left( {l + 1} \right){j_{l + 1}\left( {kr}_{q} \right)}}}{{2l} + 1}$${R_{l}^{m}\left( {\cos\quad\theta_{q}} \right)} = \left\{ \begin{matrix}\sqrt{{l\left( {l + 1} \right)}{P_{l}^{1}\left( {\cos\quad\theta_{q}} \right)}} & {{{pour}\quad m} = 0} \\{{\frac{\sqrt{\left( {l - m} \right)\left( {l + m + 1} \right)}}{2}{P_{l}^{m + 1}\left( {\cos\quad\theta_{q}} \right)}} - {\frac{\sqrt{\left( {l + m} \right)\left( {l - m + 1} \right)}}{2}{P_{l}^{m - 1}\left( {\cos\quad\theta_{q}} \right)}}} & {{{pour}\quad 1} \leq m \leq {l - 1}} \\{{- \sqrt{\frac{l}{2}}}{P_{l}^{l - 1}\left( {\cos\quad\theta_{q}} \right)}} & {{{pour}\quad m} = l}\end{matrix} \right.$and where:μ_(r)=sin θ_(q) sin θ_(q) ^(α) cos(φ_(q)−φ_(q) ^(α))+cos θ_(q) cos θ_(q)^(α)μ_(θ)=cos θ_(q) sin θ_(q) ^(α) cos(φ_(q)−φ_(q) ^(α))−sin θ_(q) cos θ_(q)^(α)μ_(φ)=sin θ_(q) ^(α) sin(φ_(q) ^(α)−φ_(q))If the acquisition means 1 comprise only cardioid sensors, the parameterd_(q) assumes the value ½ for the Q sensors.

In general, the matrix indicated E is therefore representative of theposition of the elemental sensors 2 ₁ to 2_(Q).

The determination of E does not impose any constraint on the position(r_(q),θ_(q),φ_(q)) of the sensors and in particular enables thenon-regular configurations to be taken into account. Such non-regularconfigurations are more efficient because they permit the sampling ofmore data on the initial field P, dispensing with the redundanciesintroduced by the regular configurations.

In the equation expressing T, the filtering matrix D is a decodingmatrix representative of the predetermined general reproductiondirections selected. The matrix D makes it possible to determine thecontrol signals permitting the high-precision reproduction of theestimated acoustic field {tilde over (P)} and therefore of the acquiredacoustic field P. The matrix D is of size N×(L+1)² and is obtained bymeans of the following matrix relationship:D=(M ^(T) WM)⁻¹ M ^(T) W

W is a matrix corresponding to a spatial window defining the volume inwhich the reproduction is to be carried out. It is a diagonal matrix ofsize (L+1)² which contains weighting coefficients W_(l) and in whicheach coefficient W_(l) is found 2l+1 times in succession on thediagonal. The matrix W therefore has the following form:$W = \begin{bmatrix}W_{0} & 0 & \cdots & \cdots & \cdots & \cdots & \cdots & 0 \\0 & W_{1} & ⋰ & \quad & \quad & \quad & \quad & \vdots \\\vdots & ⋰ & W_{1} & ⋰ & \quad & \quad & \quad & \vdots \\\vdots & \quad & ⋰ & W_{1} & ⋰ & \quad & \quad & \vdots \\\vdots & \quad & \quad & ⋰ & ⋰ & ⋰ & \quad & \vdots \\\vdots & \quad & \quad & \quad & ⋰ & W_{L} & ⋰ & \vdots \\\vdots & \quad & \quad & \quad & \quad & ⋰ & ⋰ & 0 \\0 & \cdots & \cdots & \cdots & \cdots & \cdots & 0 & W_{L}\end{bmatrix}$

In the embodiment described, the values assumed by the coefficientsW_(l) correspond to the values of a function such as a Hamming window ofsize 2L+1 evaluated in l, so that the parameter W_(l) is determined forl ranging from 0 to L.

M is a matrix corresponding to the predetermined general reproductiondirections, in other words, to the output multichannel format. It is amatrix of size (L+1)² by N, constituted by elements M_(l,m,n), theindices l,m denoting the line l²+l+m and n denoting the column n. Thematrix M therefore has the following form: $\begin{bmatrix}M_{0,0,1} & M_{0,0,2} & \cdots & M_{0,0,N} \\M_{1,{- 1},1} & M_{1,{- 1},2} & \cdots & M_{1,{- 1},N} \\M_{1,0,1} & M_{1,0,2} & \cdots & M_{1,0,N} \\M_{1,1,1} & M_{1,1,2} & \cdots & M_{1,1,N} \\\vdots & \vdots & \quad & \vdots \\M_{L,{- L},1} & M_{L,{- L},2} & \cdots & M_{L,{- L},N} \\\vdots & \vdots & \quad & \vdots \\M_{L,0,1} & M_{L,0,2} & \cdots & M_{L,0,N} \\\vdots & \vdots & \quad & \vdots \\M_{L,L,1} & M_{L,L,2} & \cdots & M_{L,L,N}\end{bmatrix}\quad$

In the embodiment described, the elements M_(l,m,n) are obtainedstarting from the multichannel format in accordance with therelationship:M _(l,m,n)=γ_(l) ^(m)(θ_(n),φ_(n))

where (θ_(n),φ_(n)) corresponds to the general direction associated withthe channel sc_(n)(t) in the multichannel format.

The processing step 30 therefore corresponds to the application, to theset of measurement signals c₁ to c_(Q), of filtering combinations forgenerating a plurality of processed signals constituting arepresentation {tilde over (P)} of the acoustic field P), whichrepresentation is substantially independent of the structuralcharacteristics of the acquisition means 1, in the form of a finitenumber of Fourier-Bessel coefficients.

Step 30 also corresponds to the application, to the processed signals,of specific linear combinations for generating the correspondingplurality of acoustic signals sc₁ to sc_(N).

FIG. 4 shows schematically the implementation of the processing step 30carried out by the means 8 described above.

The filters T_(n,q)(ƒ) are applied to the measurement signals c₁(t) toc_(N)(t) by means of the usual filtering methods, such as, for example:

filtering in the frequency domain, such as, for example, blockconvolution techniques;

filtering in the temporal domain by impulse response; and

filtering in the temporal domain by means of infinite impulse responserecursive filters.

The N output signals sc₁(t) to sc_(N)(t) obtained at the end of theprocessing of the invention are representative of an acoustic field{circumflex over (P)} which is reproduced by connecting each channelsc_(n)(t) to the corresponding reproduction element 12 _(n) emittingplane direction waves (θ_(d),φ_(n)) according to the specifications ofthe multichannel format. The simultaneous action of the N reproductionelements 12 ₁ to 12 _(N) controlled by the channels sc₁(t) to sc_(N)(t),respectively, enable the acoustic field {circumflex over (P)} to bereproduced.

Thanks to the processing carried out and corresponding to the filteringmatrix T, the representation of the acoustic field {circumflex over (P)}in multichannel format is close to the acoustic field P in which thesensors 2 _(q) are immersed. It appears that the matrix T is obtained bymanipulating acoustic field descriptions broken down at a high order andleads to a high-quality representation of the acoustic field.

It therefore appears that the use of a substantially non-regulardistribution of the elemental sensors enables each of the sensors to bemarked out and enables more spatial data on the acoustic field to besampled.

Thanks to the processing of the invention, all of these data can bereproduced in the best possible manner in order to obtain a high-qualityrepresentation in multichannel format with a small number of elementalsensors.

In particular, in the case of reproduction of the type referred to as5.1, as described above, the number of elemental sensors is, forexample, less than 25 and preferably less than 10.

It will be appreciated that numerous embodiments are possible.

In particular, other types of sensor may be used by modifying theequations as a function of the nature thereof. For example, all or someof the elemental sensors may be omnidirectional and/or cardioid sensors.

1. System for determining a representation of an acoustic field (P) ofthe type comprising: acoustic wave acquisition means (1) comprising aplurality of elemental sensors (2 ₁ to 2 _(Q)) which are distributed inspace and which each deliver a measurement signal (c₁ to c_(Q)); andmeans (8) for processing by the application, to the measurement signals(c₁ to c_(Q)), of filtering combinations representative of structuralcharacteristics of the acquisition means (1) in order to deliver aplurality of acoustic signals (sc₁ to sc_(N)) which are each associatedwith a predetermined general reproduction direction defined relative toa given point in space (14), the set of acoustic signals (sc₁ to sc_(N))forming a representation of the acoustic field (P), characterized inthat the elemental sensors (2 ₁ to 2 _(Q)) are distributed in space in asubstantially non-regular manner and in that the filtering combinationsare representative of that distribution.
 2. System according to claim 1,characterized in that the acquisition means (1) are such that, for allof the usual coordinate systems, for at least one of the coordinates ofthe coordinate system, the values of the coordinates of the positions ofall of the elemental sensors (2 ₁ to 2 _(Q)) are distributed on distinctvalues and at a non-constant pitch.
 3. System according to claim 1,characterized in that the acquisition means (1) comprise at least oneomnidirectional elemental sensor.
 4. System according to claim 1,characterized in that the acquisition means (1) comprise at least oneelemental sensor whose directivity is a combination of omnidirectionaland bidirectional patterns.
 5. System according to claim 1,characterized in that the acquisition means (1) comprise a number ofelemental sensors (2 ₁ to 2 _(Q)) of one to five times the number ofpredetermined general reproduction directions.
 6. System according toclaim 1, characterized in that the processing means (8) comprise asingle matrix filtering stage receiving as an input the measurementsignals (c₁ to c_(Q)) and delivering as an output the plurality ofacoustic signals (sc₁ to sc_(N)).
 7. System according to claim 6,characterized in that the processing means (8) form weighted linearcombinations of the measurement signals (c₁ to c_(Q)) in order to formthe acoustic output signals (sc₁ to sc_(N)).
 8. System according toclaim 1, characterized in that the processing means (8) permit theapplication of filtering combinations which vary with the frequency ofthe measurement signals (c₁ to c_(Q)) processed.
 9. Device fordetermining a representation of an acoustic field (P) of the type whichcomprises means (8) for processing the signals delivered by acousticwave acquisition means (1) comprising a plurality of elemental sensors(2 ₁ to 2 _(Q)) distributed in space, by applying filtering combinationsrepresentative of structural characteristics of the acquisition means(1) in order to deliver a plurality of acoustic signals (sc₁ to sc_(N))which are each associated with a predetermined general reproductiondirection defined relative to a given point in space (14), the acousticsignals (sc₁ to sc_(N)) forming a representation of the acoustic field(P), characterized in that the processing means (8) are suitable forprocessing signals delivered by acquisition means (1) formed by sensors(2 ₁ to 2 _(Q)) distributed in space in a substantially non-regularmanner.
 10. Method for determining a representation of an acoustic field(P), characterized in that it comprises: a step (20) of acquiring, at aplurality of points distributed in space in a substantially non-regularmanner, the acoustic field (P) by acoustic wave acquisition means (1) inorder to deliver a plurality of measurement signals (c₁ to c_(N)) whichare representative at each point, in amplitude and in phase, of theacoustic field (P); a step (30) of processing by applying, to themeasurement signals (c₁ to c_(Q)), filtering combinations representativeof structural characteristics of the acquisition means (1) in order todeliver a plurality of acoustic signals (sc₁ to sc_(N)) which are eachassociated with a predetermined general reproduction direction definedrelative to a given point in space (14), the set of acoustic signals(sc₁ to sc_(N)) forming a representation of the acoustic field (P). 11.Method according to claim 10, characterized in that the processing step(30) corresponds to: the application to the measurement signals (c₁ toc_(Q)) of filtering combinations in order to generate a plurality ofprocessed signals constituting a representation of the acoustic field(P) which is substantially independent of the structural characteristicsof the acquisition means (1), in the form of a finite number ofFourier-Bessel coefficients; and the application to the processedsignals of specific linear combinations in order to generate thecorresponding plurality of acoustic signals (sc₁ to sc_(N)).
 12. Methodaccording to claim 10, characterized in that the processing step (30)corresponds to the application of filtering combinations in accordancewith a technique selected from the group formed: by filtering techniquesin the frequency domain; by filtering techniques in the temporal domainby impulse response; and by filtering techniques in the temporal domainby means of infinite impulse response recursive filters.
 13. Method forchecking the non-regular character of a network of elemental sensors (2₁ to 2 _(Q)), characterized in that it consists: in considering thenetwork in a first usual coordinate system; in checking the values ofthe positions of all of the sensors (2 ₁ to 2 _(Q)) in accordance with afirst coordinate of the coordinate system; if the values of the firstcoordinates are neither constant nor distributed at regular intervals,the network is called non-regular in the current coordinate system andthe method is repeated in another coordinate system; if the values ofthe first coordinates are either constant or distributed at regularintervals, the values of the positions of the sensors are checked inaccordance with a second coordinate of the coordinate system; if thevalues of the second coordinates are neither constant, nor distributedat regular intervals, the network is non-regular in the currentcoordinate system and the method is repeated with another coordinatesystem; if the values of the second coordinates are either constant ordistributed at regular intervals, the values of the positions of thesensors are checked in accordance with a third coordinate of thecoordinate system; if the values of the third coordinates are neitherconstant, nor distributed at regular intervals, the network isnon-regular in the current coordinate system and the method is repeatedin another coordinate system; if, for the first, second and thirdcoordinates, the values of coordinates of the positions of all of thesensors are either constant or distributed at regular intervals, thenetwork is regular in the current coordinate system; if in any one ofthe usual coordinate systems, the network is regular, it is calledregular; and if the network is non-regular in each of the usualcoordinate systems, it is called non-regular.
 14. Method according toclaim 11, characterized in that the processing step (30) corresponds tothe application of filtering combinations in accordance with a techniqueselected from the group formed: by filtering techniques in the frequencydomain; by filtering techniques in the temporal domain by impulseresponse; and by filtering techniques in the temporal domain by means ofinfinite impulse response recursive filters.
 15. System according toclaim 2, characterized in that the acquisition means (1) comprise atleast one omnidirectional elemental sensor.
 16. System according toclaim 2, characterized in that the acquisition means (1) comprise atleast one elemental sensor whose directivity is a combination ofomnidirectional and bidirectional patterns.
 17. System according toclaim 2, characterized in that the acquisition means (1) comprise anumber of elemental sensors (2 ₁ to 2 _(Q)) of one to five times thenumber of predetermined general reproduction directions.
 18. Systemaccording to claim 2, characterized in that the processing means (8)comprise a single matrix filtering stage receiving as an input themeasurement signals (c₁ to c_(Q)) and delivering as an output theplurality of acoustic signals (sc₁ to sc_(N)).
 19. System according toclaim 3, characterized in that the processing means (8) comprise asingle matrix filtering stage receiving as an input the measurementsignals (c₁ to c_(Q)) and delivering as an output the plurality ofacoustic signals (sc₁ to sc_(N)).
 20. System according to claim 4,characterized in that the processing means (8) comprise a single matrixfiltering stage receiving as an input the measurement signals (c₁ toc_(Q)) and delivering as an output the plurality of acoustic signals(sc₁ to sc_(N)).